Qualitative–Quantitative Reasoning�thinking informally about formal things
Alan Dix
http://alandix.com/papers/ICTCS-QQ-2021/
@alanjohndix @CompFoundry
Tiree
Tiree Tech Wave�https://tireetechwave.org/
the foundry
building
mission
community
today I am not talking about …
Number theory�and things …
arithmetic
mathematics
?
the qualitative understanding�of quantitative phenomena
Formal models of �interactive systems
Oxymoron?
𝛌
?
=
https://en.wikipedia.org/wiki/File:The_Adicts_2011_SO36_03.jpg
PIE model – abstract properties
predict
e.g. predictability:
undo
more complex undo – the cube
PIE model – abstract properties
predict
e.g. predictability:
Insight!
Formal model often not complete or accurate
… but still gives insight
predict
Fully Charged
Electrostatically-charged crop sprays
Above canopy model
ground at�0 V
open boundary condition complex
sprayer at �high voltage
+ 1000s V
charged�spray drops
model path, speed and space voltage�due to drop cloud
?
Within Canopy Model
crop modelled as�straight sides
ground at �bottom
+V – charged spray enters crop canopy from above;�speed and charge determined by above canopy model.
Within Canopy Model
crop modelled as�straight sides
ground at �bottom
+V – charged spray enters crop canopy from above;�speed and charge determined by above canopy model.
Misses crop (Class I)
Good spread (Class II)
All at the top (Class III)
Connect and re-parameterise
+ 1000s V
above crop model
within�crop model
dimesionless�parameters
Design/engineering interventions
X
Order of magnitude�day to day
Ocean and drops
Covid and climate change
an ocean is made of drops
Covid – masks, etc.
climate & pollution
Order of magnitude�formal
Algorithmic complexity
Linear programming and sorting
What is computation?
what is computation?
information theory� entropy independent of mechanism
algorithmic complexity � measures are system dependent
sorting? – n log n lower bound� information proof – works for oracles
Galois theory feels connected?
standard Galois�field extension
ℚ
ℝ
ℚ(√2)
computational �Galois sets
ℚ0(√2)
ℚ∞(√2)
ℚ2(√2)
ℚ1(√2)
ℚ3(√2)
…
=
=
reals
rationals
rationals �extended �with solution �of x2=2
three √2 allowed
plain rationals
two √2 allowed
one √2 allowed
any number of �√2 allowed
Numerical models
As well as crop spraying …�Covid serial interval
Viral metrics
R – how many?
Serial interval – how long?
time
Viral metrics
R – how many?
Serial interval – how long?
not plain disease metrics …
time
Serial interval – 3 measures
Forward (standard)
Backward
Effective
R
t
SI
Infection time not uniform
⇒ during growth (R > 1)
backward SI < effective SI < forward SI
Monotonic reasoning
Shops to politics
Monotonic arguments
Change in shop
A – b < A
2D – Poincare property
Factory Automation
↑ more�automation
↓ less�labour needed
↑ higher�productivity
↑ higher�prosperity
↓ less�employment
↓ lower�wages
? people�better off
↑
↓
↑ more�automation
↓ decline of�other companies
↑ more�competative
↑ growth�of company
↓ less�jobs elsewhere
↑ more�jobs there
? overall�employment
↑
↓
Formalising QQR
Fuzzy logic, Bayesian methods
Allen’s interval algebra
Allen's interval algebra
A
B
A
B
precedes
meets
A
B
A
B
starts
finishes
A
B
A
B
contains
overlaps
A
B
equal
Call to arms
QQR critical for understanding …
climate change
Brexit
in short ….� being a C21 citizen
covid
Alan Dix
http://alandix.com/QQR/
@alanjohndix @CompFoundry
Qualitative–Quantitative Reasoning�thinking informally �about formal things